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A260513 a(n) = (8*n+13*n^3+3*n^5)/24; also the sum of triangular numbers taken in successive groups of increasing size (see Example). 1
1, 9, 46, 164, 460, 1091, 2289, 4376, 7779, 13045, 20856, 32044, 47606, 68719, 96755, 133296, 180149, 239361, 313234, 404340, 515536, 649979, 811141, 1002824, 1229175, 1494701, 1804284, 2163196, 2577114, 3052135, 3594791, 4212064, 4911401, 5700729, 6588470 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6) for n>6. - Colin Barker, Aug 07 2015

G.f.: x*(x^4+3*x^3+7*x^2+3*x+1) / (x-1)^6. - Colin Barker, Aug 07 2015

EXAMPLE

The first ten triangular numbers are 1,3,6,10,15,21,28,36,45,and 55.  Take them in groups, respectively, of 1, 2, 3, and 4 = (1), (3, 6), (10, 15, 21), and (28, 36, 45, 55).  Summing each group separately = 1, 9, 46, 164.

MATHEMATICA

Table[1/24*(8*x+13*x^3+3*x^5), {x, 50}]

PROG

(PARI) Vec(x*(x^4+3*x^3+7*x^2+3*x+1)/(x-1)^6 + O(x^100)) \\ Colin Barker, Aug 07 2015

CROSSREFS

Sequence in context: A280852 A009294 A061620 * A001781 A258477 A320755

Adjacent sequences:  A260510 A260511 A260512 * A260514 A260515 A260516

KEYWORD

nonn,easy

AUTHOR

Harvey P. Dale, Jul 27 2015

STATUS

approved

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Last modified November 11 18:50 EST 2019. Contains 329031 sequences. (Running on oeis4.)